Quaternionic matrix: Difference between revisions

Revision as of 21:00, 3 July 2010

Revision as of 21:04, 3 July 2010

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{{orphan|date=January 2010}}

A '''quaternionic matrix''' is a [[matrix]] whose elements are [[quaternion]]s.

== Definition ==

A quaternionic matrix is a matrix whose elements are [[quaternion]]s.

== Product of two quaternionic matrixmatrices ==

The product of two quaternionic matrixmatrices is either or hamiltonian or octonionic. The field <math>\mathbb{H}</math> is a non-commutative field , so the product of two quaternionic matrixmatrices hasmay or notmay tonot preserve the order of the multiplication .

=== Hamiltonian product ===

The hamiltonian product preserves the order of the multiplication.

:<math>

U =

\begin{pmatrix}

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\end{pmatrix}

\quad

V =

\begin{pmatrix}

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\end{pmatrix}

\quad

UV =

\begin{pmatrix}

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=== Octonionic product ===

The octonionic product does not preserve the order of the multiplication : on the main diagonal , there is an inversion of the second product and on the second diagonal there is an inversion of the first productsproduct.

<math>

U =

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== See also ==

*[[matrixMatrix]]

*[[Quaternion]]

*[[William Rowan Hamilton|Hamilton]]